a. State the null and alternative hypothesis.
b. Compute the value of the test statistic
c. What is the p-value?
d. What is your conclusion?

2. The grades of a sample of 5 students, selected from a large population, are given below.

Grade
70
80
60
90
75

a. Determine a point estimate for the variance of the population.
b. Determine a 95% confidence interval for the variance of the population.
c. At 90% confidence, test to determine if the variance of the population is
significantly more than 50.

3. Each day the major stock markets have a group of leading gainers in price (stocks that go up the most). On one day the standard deviation in the percent change for a sample of 10 NASDAQ leading gainers was 15.8. On the same day, the standard deviation in the percent change for a sample of 10 NYSE leading gainers was 7.9 (USA Today, September 14, 2000). Conduct a test for equal population variances to see whether it can be concluded that there is a difference in the volatility of the leading gainers on the two exchanges. Useα = 0.10. What is your conclusion?

4. The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:
Number of Cars Arriving
in a 10-Minute Interval Frequency
0 3
1 10
2 15
3 23
4 30
5 24
6 20
7 13
8 8
9 4

5. 7% of mutual fund investor rate corporate stocks "very safe", 58% rate them "somewhat safe", 24% rate them "not very safe", 4% rate them "not at all safe", and 7% are "not sure". A Business week/Harris poll asked 529 mutual fund investors how they would rate corporate bonds on safety. The responses are as follows.
Safety Rating Frequency
Very safe 48
Somewhat safe 323
Not very safe 79
Not at all safe 16
Not sure 63